Example 8.5 Assume that X(t) is a random process defined as follows: X(t) = A cos(2π + $) where A is a zero-mean normal random variable with variance = 2 and is a uniformly distributed random variable over the interval -≤ ≤ π. A and are statistically independent. Let the random variable Y be defined as follows: Y= = [² x X(t)dt 0 Determine 1. the mean E[Y] of Y. 2. the variance of Y.
Example 8.5 Assume that X(t) is a random process defined as follows: X(t) = A cos(2π + $) where A is a zero-mean normal random variable with variance = 2 and is a uniformly distributed random variable over the interval -≤ ≤ π. A and are statistically independent. Let the random variable Y be defined as follows: Y= = [² x X(t)dt 0 Determine 1. the mean E[Y] of Y. 2. the variance of Y.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Example 8.5 Assume that X(t) is a random process defined as follows:
X(t) = A cos(2π + $)
where A is a zero-mean normal random variable with variance o = 2 and is
a uniformly distributed random variable over the interval -≤ ≤. A and
are statistically independent. Let the random variable Y be defined as follows:
Y=
² = f*x(1)d₁
Determine
1. the mean E[Y] of Y.
2. the variance of Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc85fad51-1a38-403f-9062-c50815580d70%2F1c985b5e-0409-4648-9afd-46d9101ada0d%2Fvp0hbzj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example 8.5 Assume that X(t) is a random process defined as follows:
X(t) = A cos(2π + $)
where A is a zero-mean normal random variable with variance o = 2 and is
a uniformly distributed random variable over the interval -≤ ≤. A and
are statistically independent. Let the random variable Y be defined as follows:
Y=
² = f*x(1)d₁
Determine
1. the mean E[Y] of Y.
2. the variance of Y.
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